Downstream spatial-temporal graph neural network.
A normal downstream STGNN takes the last patch and the dependency graph as input, while the enhanced STGNN also considers the input patch's representation.
Since the TSFormer has strong power at extracting very long-term dependencies, the representation \(\mathbf {H}^i_P\)  contains rich context information.
STEP framework can extend to almost any STGNN, and we choose a representative method as our backend, the Graph WaveNet [1]}.
Graph WaveNet captures spatial-temporal dependencies efficiently and effectively by combining graph convolution with dilated casual convolution.
It makes predictions based on its output latent hidden representations \(\mathbf {H}_{gw}\in \mathbb {R}^{N\times d^{\prime }}\)  by a regression layer, which is a Multi-Layer Perception (MLP).
For brevity, we omit its details, and interested readers can refer to the paper [1]}.
Denoting the representations \(\mathbf {H}^i_P\)  of TSFormer for all node \(i\)  as \(\mathbf {H}_P\in \mathbb {R}^{N\times d}\) , we fuse the representations of Graph WaveNet and TSFormer by:
\(\mathbf {H}_{final}=\text{SP}(\mathbf {H}_P) + \mathbf {H}_{gw},\) 
